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The Thresholding Bandit Problem (TBP) aims to find the set of arms with meanrewards greater than a given threshold. We consider a new setting of TBP, wherein addition to pulling arms, one can also \emph{duel} two arms and get the armwith a greater mean. In our motivating application from crowdsourcing, duelingtwo arms can be more cost-effective and time-efficient than direct pulls. Werefer to this problem as TBP with Dueling Choices (TBP-DC). This paper providesan algorithm called Rank-Search (RS) for solving TBP-DC by alternating betweenranking and binary search. We prove theoretical guarantees for RS, and alsogive lower bounds to show the optimality of it. Experiments show that RSoutperforms previous baseline algorithms that only use pulls or duels.

Thresholding Bandit Problem with Both Duels and Pulls